A good mouser catches the mice that cross open floor, and that's real; a house with a cat that hunts will have fewer mice in the living space. But the mice that matter live inside the walls, behind the stove, in the basement ceiling and in the garage, where the cat can't go, and UC IPM notes mice seldom travel more than 30 feet from the nest to food, so a nest in the kitchen wall with a pantry next to it doesn't need to cross the living room. UC IPM's specific warning is that predators can make rodents more cryptic: the mice change their routes and timing to avoid the cat, and the household sees less evidence while the population carries on.